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Explain the following (suggested length of 1-2 pages) as if you were teaching a middle school mathematics classroom (grades 5-9):
a. Why a taxpayer whose income tax rate is 27.8% would hope that the rate could be truncated to a whole number when calculating the amount of tax owed on the tax form
1. Why the government prefers and requires the taxpayer to round the tax rate
b. Use your mental math process in calculating the above situation and how you would use rounding and truncating in real-world scenarios
1. Provide two examples of each rounding and truncation (four total examples) to illustrate mental math skills.
Relation between Cyclic Group and Abelian Group. If G is a finite group whose order is a prime number p, then G is a cyclic group. Or, Every group of prime order is cyclic. Or, Every group of prime order is abelian.
Objective questions based on regression.
Plot the data, fit a trend line, and discuss the strength of prediction of the regression model.
For each of the following vector spaces, give its dimension and a basis. The set of all symmetric 4 x 4 matrices,
Prove that the mapping a(g) = g^-1 for all g in G is an automorphism if and only if G is Abelian. An isomorphism from a group G onto itself is called an automorphism of G.
Let a be the permutation (1 2 3) in A_4. What is the order of the element (3, 7, a) in the group U(10) direct product Z_42 direct product A_4.
Consider a seven-game world series between team A and B, where for each game, what is the most likely number of games to be played in the series for p=0.6?
Let f be a non-negative monotone continuous function defined on the interval (0
Find (and describe) all the regular tessellations of the plane. Note that septagons, nonagons, and 11-gons are not provided. How do you know each one you find really fills in all the gaps around a vertex point? How do you know when you're done?
What is the probability that during a 5-minute interval no one will enter the store? What time interval is such that the probability is 1/2 that no one will enter the store during that interval?
The surface area of a pyramid is 189cm squared. The area of the sq base is 49cm squared. What is the area of one triangular face of the lateral surface?
Important information about Sets, Counting & Probability : Combinations, How many poker hands consist of four clubs and a card of a different suit?
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